Like many others I was suffering from Bluetooth connectivity problems with my Mac Mini (late 2012) which resulted in sometimes horrible mouse lags, stuttering and disconnecting. I tried everything from repeated PRAM resets to system cache cleaning, and even shutting it down for a while(!).
While I prefer not to tamper with the hardware this pointed me in the right direction: Indeed, in the course of the last years I had accumulated several external USB3 drives, and in fact the bluetooth problems have been getting worse. And, most notably, I realized that the Mac Mini was placed in a way that his back (with all the USB3 ports and cables) was pointing towards my desk.
To keep it short: I turned the Mac Mini by 90 degrees, with the cables now pointing towards the wall, and everything is fine now!
You may laugh but I’m truly excited about that! And I think it’s worth to post it since the solution was so simple that I’m sure many people don’t even consider trying it.
So, before sending the thing back to Apple, just turn it around or displace it by a feet or so. Following the logic, also a displacement of the USB3 devices might help.